Internal problem ID [818]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 4.1, Higher order linear differential equations. General theory. page 173
Problem number: 16.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 181
dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)-diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {\left (\left (188+12 \sqrt {93}\right )^{\frac {2}{3}}-4 \left (188+12 \sqrt {93}\right )^{\frac {1}{3}}+28\right ) x}{6 \left (188+12 \sqrt {93}\right )^{\frac {1}{3}}}}-c_{2} {\mathrm e}^{-\frac {\left (28+\left (188+12 \sqrt {93}\right )^{\frac {2}{3}}+8 \left (188+12 \sqrt {93}\right )^{\frac {1}{3}}\right ) x}{12 \left (188+12 \sqrt {93}\right )^{\frac {1}{3}}}} \sin \left (\frac {\left (\left (188+12 \sqrt {93}\right )^{\frac {2}{3}} \sqrt {3}-28 \sqrt {3}\right ) x}{12 \left (188+12 \sqrt {93}\right )^{\frac {1}{3}}}\right )+c_{3} {\mathrm e}^{-\frac {\left (28+\left (188+12 \sqrt {93}\right )^{\frac {2}{3}}+8 \left (188+12 \sqrt {93}\right )^{\frac {1}{3}}\right ) x}{12 \left (188+12 \sqrt {93}\right )^{\frac {1}{3}}}} \cos \left (\frac {\left (\left (188+12 \sqrt {93}\right )^{\frac {2}{3}} \sqrt {3}-28 \sqrt {3}\right ) x}{12 \left (188+12 \sqrt {93}\right )^{\frac {1}{3}}}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 87
DSolve[y'''[x]+2*y''[x]-y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-3\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-3\&,3\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-3\&,1\right ]\right ) \\ \end{align*}